Cortical traveling waves reflect state-dependent hierarchical sequencing of local regions in the human connectome network

Recent human studies using electrocorticography have demonstrated that alpha and theta band oscillations form traveling waves on the cortical surface. According to neural synchronization theories, the cortical traveling waves may group local cortical regions and sequence them by phase synchronization; however these contributions have not yet been assessed. This study aimed to evaluate the functional contributions of traveling waves using connectome-based network modeling. In the simulation, we observed stable traveling waves on the entire cortical surface wherein the topographical pattern of these phases was substantially correlated with the empirically obtained resting-state networks, and local radial waves also appeared within the size of the empirical networks (< 50 mm). Importantly, individual regions in the entire network were instantaneously sequenced by their internal frequencies, and regions with higher intrinsic frequency were seen in the earlier phases of the traveling waves. Based on the communication-through-coherence theory, this phase configuration produced a hierarchical organization of each region by unidirectional communication between the arbitrarily paired regions. In conclusion, cortical traveling waves reflect the intrinsic frequency-dependent hierarchical sequencing of local regions, global traveling waves sequence the set of large-scale cortical networks, and local traveling waves sequence local regions within individual cortical networks.

Synwalk: community detection via random walk modelling

Complex systems, abstractly represented as networks, are ubiquitous in everyday life. Analyzing and understanding these systems requires, among others, tools for community detection. As no single best community detection algorithm can exist, robustness across a wide variety of problem settings is desirable. In this work, we present Synwalk, a random walk-based community detection method. Synwalk builds upon a solid theoretical basis and detects communities by synthesizing the random walk induced by the given network from a class of candidate random walks. We thoroughly validate the effectiveness of our approach on synthetic and empirical networks, respectively, and compare Synwalk’s performance with the performance of Infomap and Walktrap (also random walk-based), Louvain (based on modularity maximization) and stochastic block model inference. Our results indicate that Synwalk performs robustly on networks with varying mixing parameters and degree distributions. We outperform Infomap on networks with high mixing parameter, and Infomap and Walktrap on networks with many small communities and low average degree. Our work has a potential to inspire further development of community detection via synthesis of random walks and we provide concrete ideas for future research.

TPSL: A propagation source localization method based on limited observation nodes

The research on localization of propagation sources on complex networks has farreaching significance in various fields. Many source localization methods have been proposed. However, the assumptions of some existing methods are too ideal, which means they cannot be widely deployed on realistic networks. In this paper, we propose a multi-source localization method TPSL based on limited observation nodes and backward diffusion-based algorithm with the consideration of heterogeneity of the propagation probabilities between nodes. Specifically, given a network topology with time and probability distributions, TPSL can infer the sources of propagation by comprehensively considering the time and probability factors in a way that accords with the characteristics of information propagation in reality. The experiments on artificial and empirical networks demonstrate that TPSL has excellent performance on these networks. We also explore the influence of different strategies of choosing observation nodes on TPSL, and find out that choosing the nodes with larger closeness centrality as observation nodes performs better. Moreover, the performance of TPSL does not be affected by the number of sources.

A Proposal for the EI Index for Fuzzy Groups

In this paper, it is proposed a measure that quantifies the relational structure within and between groups that comprehend not only the analysis of disjoint groups or non-disjoint groups but also in fuzzy groups. This measure is based on the existing measure known as the EI index. The current EI index is a measure of homophily applied to networks with the presence of disjoint groups, although disjoint groups on a large scale rarely exist in many empirical networks. The new measure permits the expansion of the analysis of social networks, for several types of attributes, and thus generating previously untapped knowledge. Moreover, it is also proposed combining edges’ and nodes’ weights in the evaluation of the EI index. The new measure is tested in two networks in different contexts. The first one is a co-authorship network, where researchers, actors in the network, are divided according to the time of completion of the doctorate. The second network is formed by trade relations between countries of the American continent, where countries are grouped according to the Human Development Index.

Plant community dynamics from the perspective of recruitment networks: introducing the Recruitment and Replacement model (R&R).

The study of plant community dynamics has a long tradition. However, this field has barely incorporated the tools developed in the modern study of ecological networks. Key for this incorporation is the availability of a theoretical model able to incorporate field data about plant-plant interactions. In this study I introduce the Recruitment and Replacement (R&R) model that explicitly incorporates empirical networks of plant-plant interactions that occur during recruitment. The R&R model is built on fundamental demographic rates and incorporates competition for space between adults, intra- and inter-specific effects of established plants on recruitment and the colonization of vacant space. The basic analysis of the model provides predictions regarding different aspects of plant community dynamics, like the environmental conditions and species properties under which facilitation of recruitment is more likely to occur, the effect of recruitment facilitation on invasion, the effects of plant-plant interactions on equilibrium abundances and community stability, and the network properties that should relate to species equilibrium abundances. Many of these predictions agree with findings from published meta-analyses, supporting the general validity of the recruitment networks framework as a general approach to integrate the study of plant community dynamics into the study of ecological networks.

The Robustness of Interdependent Directed Networks With Intra-layer Angular Correlations

The robustness of interdependent networks is a frontier topic in current network science. A line of studies has so far been investigated in the perspective of correlated structures on robustness, such as degree correlations and geometric correlations in interdependent networks, in-out degree correlations in interdependent directed networks, and so on. Advances in network geometry point that hyperbolic properties are also hidden in directed structures, but few studies link those features to the dynamical process in interdependent directed networks. In this paper, we discuss the impact of intra-layer angular correlations on robustness from the perspective of embedding interdependent directed networks into hyperbolic space. We find that the robustness declines as increasing intra-layer angular correlations under targeted attacks. Interdependent directed networks without intra-layer angular correlations are always robust than those with intra-layer angular correlations. Moreover, empirical networks also support our findings: the significant intra-layer angular correlations are hidden in real interdependent directed networks and contribute to the prediction of robustness. Our work sheds light that the impact of intra-layer angular correlations should be attention, although in-out degree correlations play a positive role in robustness. In particular, it provides an early warning indicator by which the system decoded the intrinsic rules for designing efficient and robust interacting directed networks.

Network Reconstruction in Terms of the Priori Structure Information

In this paper, we investigate the reconstruction of networks based on priori structure information by the Element Elimination Method (EEM). We firstly generate four types of synthetic networks as small-world networks, random networks, regular networks and Apollonian networks. Then, we randomly delete a fraction of links in the original networks. Finally, we employ EEM, the resource allocation (RA) and the structural perturbation method (SPM) to reconstruct four types of synthetic networks with 90% priori structure information. The experimental results show that, comparing with RA and SPM, EEM has higher indices of reconstruction accuracy on four types of synthetic networks. We also compare the reconstruction performance of EEM with RA and SPM on four empirical networks. Higher reconstruction accuracy, measured by local indices of success rates, could be achieved by EEM, which are improved by 64.11 and 47.81%, respectively.

A new approach to integrate phylogenetic structure and partner availability to study biotic specialization in ecological networks

Biotic specialization holds information about the assembly, evolution and stability of biological communities. Phylogenetic diversity metrics have been used to quantify biotic specialization, but their current implementations do not adequately account for the availability of the interacting partners. Also, the overdispersed pattern of phylogenetic specialization has been misinterpreted as an attribute of generalists. We developed an approach that resolves these issues by accounting for partner availability to quantify the phylogenetic structure of specialization (i.e., clustered, overdispersed, or random) in ecological networks. We showed that our approach avoids biases of previous methods. We also implemented it on empirical networks of host-parasite, avian seed-dispersal, lichenized fungi-cyanobacteria and coral-dinoflagellate interactions. We found a large proportion of taxa that interact with phylogenetically random partners, in some cases to a larger extent than detected with an existing method that does not account for partner availability. We also found many taxa that interact with phylogenetically clustered partners, while taxa with overdispersed partners were rare. Our results highlight the important role of randomness in shaping interaction networks, even in highly intimate symbioses, and provide a much-needed quantitative framework to assess the role that evolutionary history and symbiotic specialization play in shaping patterns of biodiversity.

Simulating Subject Communities in Case Law Citation Networks

We propose and evaluate generative models for case law citation networks that account for legal authority, subject relevance, and time decay. Since Common Law systems rely heavily on citations to precedent, case law citation networks present a special type of citation graph which existing models do not adequately reproduce. We describe a general framework for simulating node and edge generation processes in such networks, including a procedure for simulating case subjects, and experiment with four methods of modelling subject relevance: using subject similarity as linear features, as fitness coefficients, constraining the citable graph by subject, and computing subject-sensitive PageRank scores. Model properties are studied by simulation and compared against existing baselines. Promising approaches are then benchmarked against empirical networks from the United States and Singapore Supreme Courts. Our models better approximate the structural properties of both benchmarks, particularly in terms of subject structure. We show that differences in the approach for modelling subject relevance, as well as for normalizing attachment probabilities, produce significantly different network structures. Overall, using subject similarities as fitness coefficients in a sum-normalized attachment model provides the best approximation to both benchmarks. Our results shed light on the mechanics of legal citations as well as the community structure of case law citation networks. Researchers may use our models to simulate case law networks for other inquiries in legal network science.

Information Entropy Based on Propagation Feature of Node for Identifying the Influential Nodes

For understanding and controlling spreading in complex networks, identifying the most influential nodes, which can be applied to disease control, viral marketing, air traffic control, and many other fields, is of great importance. By taking the effect of the spreading rate on information entropy into account, we proposed an improved information entropy (IIE) method. Compared to the benchmark methods in the six different empirical networks, the IIE method has been found with a better performance on Kendall’s Tau and imprecision function under the Susceptible Infected Recovered (SIR) model. Especially in the Facebook network, Kendall’s Tau can grow by 120% as compared with the original IE method. And, there is also an equally good performance in the comparative analysis of imprecise functions. The imprecise functions’ value of the IIE method is smaller than the benchmark methods in six networks.